Home
Class 12
MATHS
Match the statements/expression given in...

Match the statements/expression given in Column I with the values given in Column II. Column I, Column II (p) The number of polynomials `f(x)` with non-negative integer coefficients of degree `lt=2,` satisfying `f(0)=0` and `int_0^1f(x)dx=1,i s` , 8 (q) The number of points in the interval `[-sqrt(13),sqrt(13)]` at which `f(x)=sin(x^2)+"cos"(x^2)` attains its maximum value, is, 2 (r) `int_(-2)^2(3x^2)/(1+e^x)dx` equals, 4 `(s)(int_(-2)^2cos2xdotlog((1+x)/(1-x))dx)/(int_0^ (1/2)""cos2xdotlog((1+x)/(1-x))dx)` , 0

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

The number of polynomials f(x) with non-negative integer coefficients of degree le 2 , satisfying f(0) = 0 and int_(0)^(1) f(x) dx = 1 , is

The value of ({int_(-1//2)^(1//2) cos2x.log((1+x)/(1-x))dx})/({int_(0)^(1//2)cos2x.log((1+x)/(1-x))dx}) is

If I=int_(0)^(1) (1+e^(-x^2)) dx then, s

int_(0)^(pi//2) sqrt(1- cos 2x) dx

int_(0)^(pi//2) sqrt(1- cos 2x) dx

Evaluate : (i) int_(0)^(1)(3sqrt(x^(2))-4sqrt(x))/(sqrt(x))dx , (ii) int_(0)^(1)x cos(tan^(1)x)dx

(i) int sqrt(1+ sin .(x)/(2)dx) (ii) int (1+cos 4x)/(cot x- tan x)dx

(i) int (e^(x) .(1-x))/(x^(2))dx (ii) int ((1+sin x)/(1+cos x))e^(x) dx

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. The value of lim(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi...

    Text Solution

    |

  2. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

    Text Solution

    |

  3. Match the statements/expression given in Column I with the values give...

    Text Solution

    |

  4. If int0^t(bxcos4x-asin4x)/(x^2)=(asin4t)/t-1 where 0lttltpi/4, then th...

    Text Solution

    |

  5. If I1=int0^pixf(sin^3x+cos^2x)dxa n d I2=int0^(pi/2)f(sin^3x+cos^2x)d...

    Text Solution

    |

  6. int0^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx)) dx

    Text Solution

    |

  7. If Un=int0^1x^n(2-x)^ndxa n dVn=int0^1x^n(1-x)^n dx ,n in N , and if ...

    Text Solution

    |

  8. Find the value of int0^1 2x^3-3x^2-x+1 3dxdot

    Text Solution

    |

  9. If int0^oox^(2n+1)dote^(-x^2)dx=360 , then the value of n is

    Text Solution

    |

  10. Evaluate: int0^oo(dx)/(1+x^2)

    Text Solution

    |

  11. Iflambda=int0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI2=int0...

    Text Solution

    |

  12. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf...

    Text Solution

    |

  13. Let I1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dx and I2=int(-3)^1(2(x+1)^2+1...

    Text Solution

    |

  14. Find the value of int0^(pi/2)sin2xdx

    Text Solution

    |

  15. The value of int0^(pi/2)cos^2xdx

    Text Solution

    |

  16. prove that |sint| is non-differentiable at t=pi.

    Text Solution

    |

  17. Find the value of int0^1x(1-x)dx

    Text Solution

    |

  18. Let Sn=sum(k=0)^n n/(n^2+kn+k^2) and Tn=sum(k=0)^(n-1) n/(n^2+kn+k^2) ...

    Text Solution

    |

  19. The value of the definite integral int(sqrt2-1)^(sqrt(2)+1)(x^4+x^2+2...

    Text Solution

    |

  20. If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, the...

    Text Solution

    |